Problem: Simplify the expression. $(-3q^{4}-4q^{3})(q^{4}-3q^{3}+4q^{2})$
Explanation: First use the distributive property. $ - 3 q^4 ( q^4) - 3 q^4 (-3 q^3) - 3 q^4 (4 q^2) - 4 q^3 ( q^4) - 4 q^3 (-3 q^3) - 4 q^3 (4 q^2) $ Simplify. $ - 3q^{8} + 9q^{7} - 12q^{6} - 4q^{7} + 12q^{6} - 16q^{5} $ $-3q^{8}+5q^{7}-16q^{5}$ Identify like terms. $ {- 3q^{8}} \color{#DF0030} {+ 9q^{7}} {- 12q^{6}} \color{#DF0030} {- 4q^{7}} {+ 12q^{6}} {- 16q^{5}} $ Add the coefficients. $ { -3q^{8}} \color{#DF0030} {+ 5q^{7}} { -16q^{5}} $